Question

Is the measure of ∠1 equal to the measure of ∠2? Why?

yes, because they intercept the same arc
no, because the sides of ∠2 are longer
no, because they intercept the circle at different points

Answer 1

*If you analyze the problem closely yo can see the answer is option a
the answer is yes, because they intercept the same arc*

Answer 2

Answer:  The correct option is (A) Yes, because they intercept the same arc.

Step-by-step explanation:  We are given a circle, with angles 1, 2 , 3 and 4.

We are to check whether the measure of ∠1 is equal to the measure of ∠2. If so, we are to state the reason.

According to a Circle's Theorem,  

In a circle, the measures of the angles subtended by the same arc on the circumference of the circle are equal.

In the modified attached circle,

we can see that ∠1 and ∠2 are subtended by the same arc AB at points C and D respectively on the circumference of the circle.

Therefore, their measures must be equal.

Thus,  the correct option is (A) Yes, ∠1 and ∠2 have equal measures because they intercept the same arc.